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This paper presents a significant extension of perturbation theory techniques for estimating the roots of polynomials. Building upon foundational results and recent work by Pakdemirli and Yurtsever, as well as taking inspiration from the concept of probabilistic bounds introduced by Sheikh et al., we develop and prove several novel theorems that address a wide range of polynomial structures. These include polynomials with multiple large coefficients, coefficients of different orders, alternating coefficient orders, large linear and constant terms, and exponentially decreasing coefficients. Among the key contributions is a theorem that establishes an upper bound on the expected maximum modulus of the zeros of polynomials with uniformly distributed perturbations in their coefficients. The theorem considers the case where all but the leading coefficient receive a uniformly and independently distributed perturbation in the interval [ − 1 , 1 ] . Our approach provides a comprehensive framework for estimating the order of magnitude of polynomial roots based on the structure and magnitude of their coefficients without the need for explicit root-finding algorithms. The results offer valuable insights into the relationship between coefficient patterns and root behavior, extending the applicability of perturbation-based root estimation to a broader class of polynomials. This work has potential applications in various fields, including random polynomials, control systems design, signal processing, and numerical analysis, where quick and reliable estimation of polynomial roots is crucial. Our findings contribute to the theoretical understanding of polynomial properties and provide practical tools for engineers and scientists dealing with polynomial equations in diverse contexts. [ABSTRACT FROM AUTHOR]

This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model. [ABSTRACT FROM AUTHOR]

With advanced digital technologies as the key support, many scholars and researchers have proposed various random warranty models by integrating mission cycles into the warranty stage. However, these existing warranty models are designed only from the manufacturer's subjective perspective, ignoring certain consumer requirements. For instance, they overlook a wide range of warranty coverage, the pursuit of reliability improvement rather than mere minimal repair, and the need to limit the delay in repair. To address these consumer requirements, this paper proposes a novel random collaborative preventive maintenance warranty with repair-time threshold (RCPMW-RTT). This model incorporates terms that are jointly designed by manufacturers and consumers to meet specific consumer needs, thereby overcoming the limitations of existing warranty models. The introduction of a repair-time threshold aims to limit the time delay in repairing failures and to compensate for any losses incurred by consumers. Using probability theory, the RCPMW-RTT is evaluated in terms of cost and time, and relevant variants are derived by analyzing key parameters. As an exemplary representation of the RCPMW-RTT, two random replacement policies named the discrete random renewable back replacement (DRRBR) and the discrete random renewable front replacement (DRRFR) are proposed and modelled to ensure reliability after the expiration of the RCPMW-RTT. In both policies, product replacement is triggered either by the occurrence of the first extreme mission cycle or by reaching the limit on the number of non-extreme mission cycles, whichever comes first. Probability theory is used to present cost rates for both policies in order to determine optimal values for decision variables. Finally, numerical analysis is performed on the RCPMW-RTT to reveal hidden variation tendencies and mechanisms; numerical analysis is also performed on the DRRBR and the DRRFR. The numerical results show that the proposed random replacement policies are feasible and unique; the replacement time within the post-warranty coverage increases as the maintenance quality improves and the cost rate can be reduced by setting a smaller repair-time threshold. [ABSTRACT FROM AUTHOR]

In this study, we investigate different epidemic control scenarios through theoretical analysis and numerical simulations. To account for two important types of control at the early ascending stage of an outbreak, nonmedical interventions, and medical treatments, a compartmental model is considered with the first control aimed at lowering the disease transmission rate through behavioral changes and the second control set to lower the period of infectiousness by means of antiviral medications and other forms of medical care. In all experiments, the implementation of control strategies reduces the daily cumulative number of cases and successfully "flattens the curve". The reduction in the cumulative cases is achieved by eliminating or delaying new cases. This delay is incredibly valuable, as it provides public health organizations with more time to advance antiviral treatments and devise alternative preventive measures. The main theoretical result of the paper, Theorem 1, concludes that the two optimal control functions may be increasing initially. However, beyond a certain point, both controls decline (possibly causing the number of newly infected people to grow). The numerical simulations conducted by the authors confirm theoretical findings, which indicates that, ideally, around the time that early interventions become less effective, the control strategy must be upgraded through the addition of new and improved tools, such as vaccines, therapeutics, testing, air ventilation, and others, in order to successfully battle the virus going forward. [ABSTRACT FROM AUTHOR]

In this paper, we present an electric field analysis for the optimal structural design of lightning rods for high performance with a charge transfer system (CTS). In the case of a conventional rod that is produced with an empirical design and structure without quantitative data because the design is structurally very simple, only the materials and radius of curvature of the lightning rod to concentrate the electric field at the tip part of the rod are considered. Recently, the development of new types of lightning rods, such as early streamer emission (ESE) and charge transfer system (CTS), has been introduced through simulation analysis and experiments, but detailed specifications and information about the optimal design and structure have not been fully reported. In this paper, we performed an electric field analysis of the structures and materials for the optimal structural design of lightning rods with a function of CTS through computer software analysis with consideration for the radius of curvature, the size of corona ring, and optimal position (X-axis and Y-axis) of the floating electrode. For optimal structural design of lightning rods based on electric field analysis, we used a source of lightning voltage with 1.2/50 µs based on a double exponential equation. The results revealed that the electric field on the relaxation part decreases as the radius of curvature and corona ring increases. For the radius of curvature, the electric field first decreases and then increases with increasing radius of curvature and reaches a minimum at 7 mm and a maximum above 8 mm. For the case of the corona ring, the electric field decreases with increasing corona ring, and the optimal size of the corona ring was selected as 4 mm; the size of the 4 mm corona ring uniformly formed the electric field both at the tip part of the ground current collector and the corona ring. For the electric field concentration part, we found that the optimal X-axis position of the floating electrode and the Y-axis position between the ionizer conductor and floating electrode are 7 mm and 0.1 mm, respectively. These simulation results in this paper are expected to provide useful information for the design of optimized CTS-type lightning rods. [ABSTRACT FROM AUTHOR]

This work explores a well-established eighth-algebraic-order numerical method belonging to the explicit Numerov-type family. To enhance its efficiency, we integrated a cost-effective algorithm for adjusting the step size. After each step, the algorithm either maintains the current step length, halves it, or doubles it. Any off-step points required by this technique are calculated using a local interpolation function. Numerical tests involving diverse problems demonstrate the significant efficiency improvements achieved through this approach. The method is particularly effective for solving differential equations with oscillatory behavior, showcasing its ability to maintain high accuracy with fewer function evaluations. This advancement is crucial for applications requiring precise solutions over long intervals, such as in physics and engineering. Additionally, the paper provides a comprehensive MATLAB-R2018a implementation, facilitating ease of use and further research in the field. By addressing both computational efficiency and accuracy, this study contributes a valuable tool for the numerical analysis community. [ABSTRACT FROM AUTHOR]

For the generalized Sturm–Liouville problem (GSLP), a new formulation is undertaken to reduce the number of unknowns from two to one in the target equation for the determination of eigenvalue. The eigenparameter-dependent shape functions are derived for using in a variable transformation, such that the GSLP becomes an initial value problem for a new variable. For the uniqueness of eigenfunction an extra condition is imposed, which renders the right-end value of the new variable available; a derived implicit nonlinear equation is solved by an iterative method without using the differential; we can achieve highly precise eigenvalues. For the nonlocal Sturm–Liouville problem (NSLP), we consider two types of integral boundary conditions on the right end. For the first type of NSLP we can prove sufficient conditions for the positiveness of the eigenvalue. Negative eigenvalues and multiple solutions may exist for the second type of NSLP. We propose a boundary shape function method, a two-dimensional fixed-quasi-Newton method and a combination of them to solve the NSLP with fast convergence and high accuracy. From the aspect of numerical analysis the initial value problem of ordinary differential equations and scalar nonlinear equations are more easily treated than the original GSLP and NSLP, which is the main novelty of the paper to provide the mathematically equivalent and simpler mediums to determine the eigenvalues and eigenfunctions. [ABSTRACT FROM AUTHOR]

Interval demand is becoming more common than ever before, since the variation bounds of uncertain demand are only required in practice, and they could be obtained through only a small amount of uncertain information. The goal of this paper is to analyze the optimal decision and coordination of a competitive dual-channel supply chain under an interval uncertain demand. For this purpose, we establish a centralized decision model and a wholesale price contract model under both interval demand and channel competition, respectively. Meanwhile, both the satisfaction degree of interval and the order relation of interval number are proposed to convert interval uncertain optimization problems to deterministic ones. Then, we derive the optimal pricing decisions, ordering quantities, and performances of partners and the supply chain system. Meanwhile, a revenue sharing contract is proposed to coordinate the competitive dual-channel supply chain under interval demand. Moreover, we found that the bounds of interval demand and channel sensitivities affect the optimal strategies and revenue sharing contract under interval uncertainty. Finally, we present a numerical analysis to illustrate the proposed results in this paper and conduct sensitivity analyses. The findings of this paper provide important references for decision makers and managers to make scientific decisions in an interval uncertain environment. [ABSTRACT FROM AUTHOR]

Vehicle velocity prediction (VVP) plays a pivotal role in determining the power demand of hybrid electric vehicles, which is crucial for establishing effective energy management strategies and, subsequently, improving the fuel economy. Neural networks (NNs) have emerged as a powerful tool for VVP, due to their robustness and non-linear mapping capabilities. This paper describes a comprehensive exploration of NN-based VVP methods employing both qualitative theory analysis and quantitative numerical simulations. The used methodology involved the extraction of key feature parameters for model inputs through the utilization of Pearson correlation coefficients and the random forest (RF) method. Subsequently, three distinct NN-based VVP models were constructed comprising the following: a backpropagation neural network (BPNN) model, a long short-term memory (LSTM) model, and a generative pre-training (GPT) model. Simulation experiments were conducted to investigate various factors, such as the feature parameters, sliding window length, and prediction horizon, and the prediction accuracy and computation time were identified as key performance metrics for VVP. Finally, the relationship between the model inputs and velocity prediction performance was revealed through various comparative analyses. This study not only facilitated the identification of an optimal NN model configuration to balance prediction accuracy and computation time, but also serves as a foundational step toward enhancing the energy efficiency of hybrid electric vehicles. [ABSTRACT FROM AUTHOR]

( R , S )-(skew) symmetric matrices have numerous applications in civil engineering, information theory, numerical analysis, etc. In this paper, we deal with the ( R , S )-(skew) symmetric solutions to the quaternion matrix equation A X B = C . We use a real representation A τ to obtain the necessary and sufficient conditions for A X B = C to have ( R , S )-(skew) symmetric solutions and derive the solutions when it is consistent. We also derive the least-squares ( R , S )-(skew) symmetric solution to the above matrix equation. [ABSTRACT FROM AUTHOR]

In the field of finance and insurance, addressing the optimal investment and reinsurance issue is a focal point for researchers. This paper contemplates the optimal strategy for insurance companies within a model where wealth dynamics adhere to a jump–diffusion process. The fractional structure of the diffusion term is extremely interpretative. This model encompasses elements of risky assets, risk-free assets, and proportional reinsurance. Based on this model and grounded in the principles of stochastic control, the corresponding HJB equation is derived and solved. Consequently, explicit expressions for the optimal investment and reinsurance ratios are obtained, and the solution's verification theorem is proven. Finally, through a numerical analysis with varying parameters, results consistent with real-world scenarios are achieved. [ABSTRACT FROM AUTHOR]

Blockchain-based federated learning (BCFL) has been regarded as an emerging data sharing paradigm in edge networks of internet-of-things (IoT) because of its advantages, such as decentralization, collaborative model training, and privacy protection. However, there have been few studies focusing on strategic analysis in the BCFL system, which is important for establishing a robust and sustainable BCFL system in an untrustworthy and profit-driven environment. In this paper, we first propose a self-organizing data sharing system supported by BCFL to deeply analyze the data sharing logic. Then, a mathematical model based on evolutionary game theory is established to analyze the interaction between model owners and data providers, aiming at exploring the stability of user strategies under different considerations. According to the strategic analysis, we designed and further discussed a dynamic system control mechanism based on smart contracts to adaptively maintain a robust and sustainable BCFL system. We conducted numerical analysis and experiments to verify our work. [ABSTRACT FROM AUTHOR]

In this paper, a simplified discrete-time SIR model with nonlinear incidence and recovery rates is discussed. Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurcations (fold-flip bifurcation, 1:3 resonance, and 1:4 resonance) of the simplified discrete-time SIR model in detail by bifurcation theory and numerical continuation techniques. Parameter conditions for the occurrence of codimension-two bifurcations are obtained by constructing the corresponding approximate normal form with translation and transformation of several parameters and variables. To further confirm the accuracy of our theoretical analysis, numerical simulations such as phase portraits, bifurcation diagrams, and maximum Lyapunov exponents diagrams are provided. In particular, the coexistence of bistability states is observed by giving local attraction basins diagrams of different fixed points under different integral step sizes. It is possible to more clearly illustrate the model's complex dynamic behavior by combining theoretical analysis and numerical simulation. [ABSTRACT FROM AUTHOR]

This paper deals with numerical analysis of solutions to stochastic differential equations with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic real-valued function that satisfies a second-order differential equation. The Euler–Maruyama scheme is used to approximate the solution to the equations. It is shown that the rate of convergence is 1 2 . Numerically, two different methods are used to approximate solutions for this class of SDEJs. The first method is the direct approximation of the original equation using the Euler–Maruyama scheme with specific tests for the evaluation of the singular part at simulated values of the solution. The second method consists of taking the inverse of the Euler–Maruyama approximation for Zvonkin's transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical methods is carried out. Theoretical results are illustrated and proved by means of an example. [ABSTRACT FROM AUTHOR]

The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this paper, we not only extend the axiomatic definition of the knowledge measure of the interval-valued intuitionistic fuzzy set to a more general level but also establish a new knowledge measure function complying with the distance function combined with the technique for order preference by similarity to ideal solution (TOPSIS). Further, we investigate the properties of the proposed knowledge measure based on mathematical analysis and numerical examples. In addition, we create the entropy function by calculating the distance from the interval-valued fuzzy set to the most fuzzy point and prove that it satisfies the axiomatic definition. Finally, the proposed entropy is applied to the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy information. Experimental results demonstrate the effectiveness and practicability of the proposed entropy measure. [ABSTRACT FROM AUTHOR]

Depending on the connection type, especially semi-rigid connections, the analyses of building structures offer accurate results function of the rigidity and ductility. The present paper analyzes the in-line connection of rectangular and circular hollow sections, categorized as semi-rigid connections, suitable for an architectural design of invisible joints. For such connection the standards do not cover an explicit design method. Experimental bending tests were performed on rectangular and circular hollow sections having the end plate fixed inside the profile and bolted by four and one high-strength bolts, respectively. The joint separation represents a serviceability criterion which was monitored using digital image correlation technique. Based on experimental results, a numerical model was validated using the finite element method. After the validation of the numerical model based on the experimental results, a parametric investigation was conducted to study the influence of the access hole, the preload level, the end plate thickness, and the axial force. The results show the small influence of the bolt preload, but the end plate thickness was of major importance. A reduction of the assembly rigidity was also caused by the manhole. The study shows the feasibility of the connection configuration with the end plate positioned inside the hollow profile. [ABSTRACT FROM AUTHOR]

The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous theoretical analysis and according to the mechanical relationships, the principle of equilibrium, the material constitutive law, and the strain/displacement compatibility equation are used to deduce the closed-form analytical solution of the stress/displacement of the rock mass in the plastic region and to complete the simulation and interpretation of the nonlinear behavior of surrounding rock due to the advancing excavation of a circular tunnel. In this paper, confinement loss is regarded as the concept of increment in numerical analysis, and the calculation process and analysis steps of the explicit analysis method (EAM) are proposed. This method can not only realize the calculation of analytical solutions but can also be performed using simple spreadsheets. In addition, to verify the feasibility of this calculation method, this study uses published data to verify the validity of the analytical solution implemented by the incremental procedure and to study the influence of nonlinear failure criteria on the GRC, especially the mechanical behavior at the intrados of the tunnel and the distributions of tress/displacement on the cross-section of the tunnel. A comparison between the published results and the proposed solution in this study reveals consistent and favorable trends. [ABSTRACT FROM AUTHOR]

In this paper, the two-step method is considered with the generalized Newton method as a predictor step. The three-point Newton–Cotes formula is taken as a corrector step. The proposed method's convergence is discussed in detail. This method is very simple and therefore very effective for solving large systems. In numerical analysis, we consider a beam equation, transform it into a system of absolute value equations and then use the proposed method to solve it. Numerical experiments show that our method is very accurate and faster than already existing methods. [ABSTRACT FROM AUTHOR]

The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models. [ABSTRACT FROM AUTHOR]

To protect our environment, current firms are committed to the circular economy and process maintenance strategies to reduce the waste of resources. In this way, they can also save costs and create an enterprise image and value. Therefore, this study explores an imperfect production system with a circular economy and process maintenance activities, wherein the defective products can be converted into scrap returns (i.e., secondary raw materials) and products can be manufactured using mixed materials containing scrap returns. The proposed system considers multiple products with varying feed rates of scrap returns. According to the scenario of the aforementioned production system, this paper develops a production–inventory model aimed at cost minimization, in which the production run time, purchased quantity of material, number of maintenance times, and recovery rate are decision variables. Furthermore, we also develop a computational algorithm to obtain these optimal solutions efficiently. Finally, the numerical and sensitivity analyses based on a practical case are presented to illustrate the applicability of our method and some managerial implications. For example, both strategies efficiently reduce the total cost per unit time in the proposed numerical example. The sensitivity results can be used to determine the optimal combination of two strategies and the execution moment under various changes in cost parameters. [ABSTRACT FROM AUTHOR]

This paper proposed an efficient and adaptive frequency sampling algorithm for frequency response analysis using dynamic condensation-based reduced-order modeling. For the degree of freedom-based model reduction method, the reduced-order basis becomes a frequency-dependent matrix since the relationship between master and slave degrees of freedom stems from partial equations of a second-order dynamical system. Such frequency-dependency makes the analysis inefficient for investigating the frequency response of the system. Considering that the coverage of a local reduced-order basis at a single frequency varies depending on the frequency, a new frequency sampling algorithm was proposed with a strategy of constructing multiple local reduced-order models (ROMs) at sample frequencies. For adaptive sampling, the frequency range of a local ROM was evaluated, and a new sample was added if there was a gap between two adjacent ROMs. As a result, the accuracy of the local ROM can be estimated, and the efficiency in the online stage was greatly enhanced. The proposed method was verified by performing frequency response analysis with several numerical examples, including a large-scale structural and dynamic system. [ABSTRACT FROM AUTHOR]

The paper analyses dynamical growth models predicting the cyclic development of investigated economic factors. The provided research deals with an optimal control problem based on the economic growth model with the production function of Cobb–Douglas type. Following the Pontryagin maximum principle, we derived the Hamiltonian system and conducted its qualitative analysis, which reveals conditions for the cyclic behaviour of the optimal solutions around the isolate steady state. Numerical experiments visually illustrated the obtained results by demonstrating a phase portrait corresponding to a steady state of the focal type. [ABSTRACT FROM AUTHOR]

The huge traffic of e-commerce platforms provides a wide market for stores, but the fierce competition among stores for onsite traffic increases the cost of onsite promotion for stores, and it also reduces the effectiveness of promotion. Therefore, more and more stores on e-commerce platforms are using content platforms for offsite promotion. In the face of stores' onsite and offsite promotion behaviors, the choice of competition and cooperation strategies among participants in the promotion process is the key to solving the problem of increasing traffic. Accordingly, this paper constructs an onsite and offsite promotion decision model consisting of an e-commerce platform, a store on the e-commerce platform, and a content platform, and it compares the results based on the decentralized decision situation, centralized decision situation, and promotion investment sharing situation. In addition, some results are presented in more detail in the form of numerical analysis. The results show that the promotion investment sharing does not change the level of onsite promotion investment, but the centralized decision makes the onsite promotion investment decrease; promotion investment sharing and centralized decision scenarios increase the promotion investment of the e-commerce platform and the content platform. When the sum of the parts of promotion investments shared by the store and the content platform for the e-commerce platform is relatively small, each participant will be willing to participate in the promotion investment sharing agreement. We believe that this study will provide important implications for the resolution of stores' traffic dilemmas on e-commerce platforms. [ABSTRACT FROM AUTHOR]

In this paper, an iterative method was considered for solving the absolute value equation (AVE). We suggest a two-step method in which the well-known Gauss quadrature rule is the corrector step and the generalized Newton method is taken as the predictor step. The convergence of the proposed method is established under some acceptable conditions. Numerical examples prove the consistency and capability of this new method. [ABSTRACT FROM AUTHOR]

There are few examples of mechanical coupling solutions for the transmission of high torques between two rotating shafts that have non-coplanar, non-parallel axes. Based on the structural analysis, the paper proposes a solution for an RP1PR-type symmetrical coupling. The Hartenberg–Denavit methodology is not applicable for performing the kinematical analysis, hence the solution starts from the geometrical condition of the creation of planar pairs of the mechanism, expressed in vector form. The absolute motion of all elements of the mechanism's structure can be expressed after developing the kinematical analysis. The theoretical results are validated via numerical analysis. By comparing the analytical results with the CATIA-modeled results, excellent compatibility is obtained. We also propose a constructive solution for the newly designed coupling mechanism. [ABSTRACT FROM AUTHOR]

Core acquisition is essential to the success of the remanufacturing business. The value of sorting and grading cores into nominal-quality classes has been certified in industry and academia. In this paper, we investigate how many unsorted cores of uncertain quality should be acquired and how many sorted cores should be remanufactured by a third-party remanufacturer (3PR) before the demand is realized. We first develop analytically tractable solutions to the acquisition and production model under deterministic demand, and then we extend it to the model under the stochastic demand by fully characterizing the structure of the optimal policy. Subsequently, we investigate the impact of core quality fraction uncertainty on the solutions. Finally, numerical analyses are conducted to further verify the proposed models. The results are as follows. First, the optimal quantity of acquisition/production and minimum expected profit increase with an increase in the selling price and decrease with an increase in the uncertainty of demand and acquisition cost. Second, the optimal production quantity does not decrease in acquisition quantity, and the rate of utilization of the recycled parts (the ratio of production quantity to acquisition quantity) increases with a decrease in the acquisition cost. Third, the growth stage is most profitable stage, so the remanufacturers should pay more attention to remanufacturing activities early in the life of products. The proposed models and solutions can not only solve the core acquisition and production problem in remanufacturing, but also solve the combinatorial optimization problem. [ABSTRACT FROM AUTHOR]

In this paper, we analyze, from the numerical point of view, a swelling porous thermo-elastic problem. The so-called second-sound effect is introduced and modeled by using the simplest Maxwell–Cattaneo law. This problem leads to a coupled system which is written by using the displacements of the fluid and the solid, the temperature and the heat flux. The numerical analysis of this problem is performed applying the classical finite element method with linear elements for the spatial approximation and the backward Euler scheme for the discretization of the time derivatives. Then, we prove the stability of the discrete solutions and we provide an a priori error analysis. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximations, the exponential decay of the discrete energy and the dependence on a coupling parameter. [ABSTRACT FROM AUTHOR]

Probability-based distributions might be able to explain risk exposure well. Usually, one number, or at the very least, a limited number of numbers called the key risk indicators (KRIs), are used to describe the level of risk exposure. These risk exposure values, which are undeniably the outcome of a specific model, are frequently referred to as essential critical risk indicators. Five key risk indicators, including value-at-risk, tail variance, tail-value-at-risk, and tail mean-variance, were also used for describing the risk exposure under the reinsurance revenues data. These measurements were created for the proposed model; hence, this paper presents a novel distribution for this purpose. Relevant statistical properties are derived, including the generating function, ordinary moments, and incomplete moments. Special attention is devoted to the applicability of the new model under extreme data sets. Three applications to real data show the usefulness and adaptability of the proposed model. The new model proved its superiority against many well-known related models. Five key risk indicators are employed for analyzing the risk level under the reinsurance revenues dataset. An application is provided along with its relevant numerical analysis and panels. Some useful results are identified and highlighted. [ABSTRACT FROM AUTHOR]

The delay differential equations are of great importance in real-life phenomena. A special type of these equations is the Pantograph delay differential equation. Generally, solving a delay differential equation is a challenge, especially when the complexity of the delay terms increases. In this paper, the homotopy perturbation method is proposed to solve the Pantograph delay differential equation via two different canonical forms; thus, two types of closed-form solutions are determined. The first gives the standard power series solution while the second introduces the exponential function solution. It is declared that the current solution agrees with the corresponding ones in the literature in special cases. In addition, the properties of the solution are provided. Furthermore, the results are numerically validated through performing several comparisons with the available exact solutions. Moreover, the calculated residuals tend to zero, even in a huge domain, which reflects the high accuracy of the current analysis. The obtained results reveal the effectiveness and efficiency of the current analysis which can be further extended to other types of delay equations. [ABSTRACT FROM AUTHOR]

The squeeze film effect was discussed in several fields, but mostly under the same pressure boundary conditions. However, pressures at the inlet and outlet are different for aerostatic bearings. In this paper, the dynamic Reynolds equation group, with the stiffness and damping pressure written separately, is deducted and numerically solved with a high-pressure boundary for a parallel flat and circular thin film. The circular thin film considers the two results of the supply pressure boundary inside and outside. All dynamic pressure distribution and stiffness curves are given in a dimensionless form, and a comparative analysis of squeeze film characteristics with and without external pressure is conducted. From the calculation results, it can be concluded that the squeeze effect shows damping for zero-frequency and stiffness for infinite-frequency for compressible lubricants. The dynamic pressure in the static high pressure region is also high at high frequencies affected by gas compressibility. Based on these analytical results, the transfer functions of the thin film are given to further analyze the dynamic performance of aerostatic bearings, and the shape of the response curve approximates an exponential decay form, even when the amplitude increases to 10% of the gas film thickness. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional simplified Hodgkin–Huxley model under exposure to electric fields. The Hopf bifurcations of the simplified Hodgkin–Huxley model are investigated through qualitative analysis and numerical simulations. A necessary and sufficient condition for the existence of Hopf bifurcations is derived, and the conditions for supercritical and subcritical Hopf bifurcations are obtained. Finally, bifurcation diagrams are given for two parameters, and numerical examples are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The computation of the time-varying matrix pseudoinverse has become crucial in recent years for solving time-varying problems in engineering and science domains. This paper investigates the issue of calculating the time-varying pseudoinverse based on full-rank decomposition (FRD) using the zeroing neural network (ZNN) method, which is currently considered to be a cutting edge method for calculating the time-varying matrix pseudoinverse. As a consequence, for the first time in the literature, a new ZNN model called ZNNFRDP is introduced for time-varying pseudoinversion and it is based on FRD. Five numerical experiments investigate and confirm that the ZNNFRDP model performs as well as, if not better than, other well-performing ZNN models in the calculation of the time-varying pseudoinverse. Additionally, theoretical analysis and numerical findings have both supported the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

Considering that the state transfer rules between nodes in existing rumor propagation models are mostly based on a single propagation mechanism, and most of the models have a single way of refuting rumors, in this paper, a new SEIOR rumor propagation model (ignorant (S), hesitators (E), spreaders (I), rumor debunkers (O), immunizers (R)) is proposed by introducing hesitators and rumor debunkers and combining different rumor-refuting ways of rumor debunkers. Firstly, the dynamics process of the propagation model is described by using the mean-field equations. Secondly, the equilibrium point and the basic regeneration number of the model are solved, and the existence and stability of the equilibrium point are discussed. Then, numerical simulations are used to analyze the effects of different factors on rumor propagation patterns. The results show that the rumor-spreading rate α 2 has the greatest effect on rumor propagation. With the increase in α 2 , the degree of influence of the hesitator-converting rate α 1 on the scale of rumor propagation first increases and then decreases. Different rumor-refuting ways have different inhibiting effects on the spread of rumors. Finally, based on the results of the theoretical proving and numerical analysis, some targeted measures to control the spread of rumors are proposed. [ABSTRACT FROM AUTHOR]

Business process anomalous behavior detection reveals unexpected cases from event logs to ensure the trusted operation of information systems. Anomaly behavior is mainly identified through a log-to-model alignment analysis or numerical outlier detection. However, both approaches ignore the influence of probability distributions or activity relationships in process activities. Based on this concern, this paper incorporates the behavioral relationships characterized by the process model and the joint probability distribution of nodes related to suspected anomalous behaviors. Moreover, a Petri Net-Based Bayesian Network (PN-BBN) is proposed to detect anomalous behaviors based on the probabilistic inference of behavioral contexts. First, the process model is filtered based on the process structure of the process activities to identify the key regions where the suspected anomalous behaviors are located. Then, the behavioral profile of the activity is used to prune it to position the ineluctable paths that trigger these activities. Further, the model is used as the architecture for parameter learning to construct the PN-BBN. Based on this, anomaly scores are inferred based on the joint probabilities of activities related to suspected anomalous behaviors for anomaly detection under the constraints of control flow and probability distributions. Finally, PN-BBN is implemented based on the open-source frameworks PM4PY and PMGPY and evaluated from multiple metrics with synthetic and real process data. The experimental results demonstrate that PN-BBN effectively identifies anomalous process behaviors and improves the reliability of information systems. [ABSTRACT FROM AUTHOR]

This paper appertains the presentation of a Clenshaw–Curtis rule to evaluate highly oscillatory Fredholm integro-differential equations (FIDEs) with Cauchy and weak singularities. To calculate the singular integral, the unknown function approximated by an interpolation polynomial is rewritten as a Taylor series expansion. A system of linear equations of FIDEs obtained by using equally spaced points as collocation points is solved to obtain the unknown function. The proposed method attains higher accuracy rates, which are proven by error analysis and some numerical examples as well. [ABSTRACT FROM AUTHOR]

The current journal paper proposes an end-to-end analysis for the numerical implementation of a two-degrees-of-freedom (2DOF) control structure, starting from the sampling rate selection mechanism via a quasi-optimal manner, along with the estimation of the worst-case execution time (WCET) for the specified controller. For the sampling rate selection, the classical Shannon–Nyquist sampling theorem is replaced by an optimization problem that encompasses the trade-off between the fidelity of the controllers' representation, along with the fidelity of the resulting closed-loop systems, and the implementation difficulty of the controllers. Additionally, the WCET analysis can be seen as a verification step before automatic code generation, a computational model being provided. The proposed computational model encompasses infinite-impulse response (IIR) and finite-impulse response (FIR) filter models for the controller implementation, along with additional relevant phenomena being discussed, such as saturation, signal scaling and anti-windup techniques. All proposed results will be illustrated on a DC motor benchmark control problem. [ABSTRACT FROM AUTHOR]

Multi-skilled resources have brought more flexibility to resource scheduling and have been a key factor in the research of resource-constrained project scheduling problems. However, existing studies are mainly limited to deterministic problems and neglect some uncertainties such as resource breakdowns, while resource availability may change over time due to unexpected risks such as the COVID-19 pandemic. Therefore, this paper focuses on the multi-skilled project scheduling problem with uncertainty in resource availability. Different from previous assumptions, multi-skilled resources are allowed a switch in their skills, which we call dynamic skill assignment. For this complex problem, a nested dynamic scheduling algorithm called GA-PR is proposed, which includes three new priority rules to improve the solving efficiency. Moreover, the algorithm's effectiveness is verified by an example, and the modified Project Scheduling Problem Library (PSPLIB) is used for numerical experimental analysis. Numerical experiments show that when the uncertainty in resource availability is considered, the more skills the resource has and the more resources are supplied, the better the dynamic scheduling method performs; on the other hand, the higher the probability of resource unavailability and the more skills are required, the worse the dynamic scheduling method performs.The results are helpful for improved decision making. [ABSTRACT FROM AUTHOR]

This paper contains two parts: numerical analyses and a control method. The numerical analyses of a hypersonic flying object's aerodynamic heating environment are based on three different two-dimensional outflow fields via finite element calculations. Then, the reference temperature trajectories of a hypersonic flying object are obtained. The other one is an intelligent proportional-derivative (IPD) with a nonlinear global sliding mode control (NGSMC) based on a nonlinear extended state observer (NESO) for a real-time ground aerodynamic heating simulation of a hypersonic flying object, named a thermal-structural test with quartz lamp heaters. The composite controller is made of three sub-components: a model free frame that is independent of the system dynamic model along with an ultra-local model; a NESO for the lumped disturbances observation; and an integral sliding mode control with a nonlinear function for the observation errors compensation. The flight environment of the hypersonic flying object is from Mach number 0.6 to Mach number 5.0, with between flight altitude of 31,272 m and flight altitude of 13,577 m. The comparative results demonstrate some superiorities of the proposed composite controller in terms of tracking errors and robustness. [ABSTRACT FROM AUTHOR]

This paper developed a quantitative evaluation necessary to ensure ground stability, so a quantitative indicator (bearing capacity). A homogeneous axisymmetric model was generated, considering China's stress field and the Karst topography characteristics, simultaneously obtaining stress component expression. We then determined the bearing capacity calculation formula by combining the strength theory of shear failure and the stress component expressions. Finally, the comparison of the bearing capacity calculation results between theoretical analysis and a numerical simulation indicated that the error was less than 5%, and the result verified the rationality of the formula. [ABSTRACT FROM AUTHOR]

Increasing energy needs, pollution of nature, and eventual depletion of resources have prompted humanity to obtain new technologies and produce energy using clean sources and renewables. In this paper, we design an advanced method to improve the performance of a sliding mode controller combined with control theory for a photovoltaic system. Specifically, we decouple the controlled output of the system from any perturbation source and assess the effectiveness of the results in terms of solution quality, closed-loop control stability, and dynamical convergence of the state variables. This study focuses on the climatic conditions that may affect the behavior of a solar energy plant to supply a motor with the highest possible efficiency and nominal operating conditions. The designed method enables us to obtain an optimal performance by means of advanced control techniques and a slime mould stochastic optimization algorithm. The efficiency and performance of this method are examined based on a benchmark model of a photovoltaic system via numerical analysis and simulation. [ABSTRACT FROM AUTHOR]

This paper proposes a general design method for cams based on the kinematics and dynamics of a mechanical system. According to the actuator's trajectory, the cam profile is generated in reverse based on the kinematic model of the system. Firstly, the cam design's optimising problem is converted into the execution trajectory's optimisation to obtain the optimum operation trajectory according to the actuator's requirements. Secondly, the relationship between the cam profile and the actuation trajectory is modelled based on the kinematics and dynamics of the mechanical system. Then, applying the cubic spline interpolation method, the cam profile is generated, and the error compensation methods are illustrated through numerical analysis. Finally, the validity of the presented design method is verified through experiments, which demonstrate the reliability of this method. [ABSTRACT FROM AUTHOR]

In this paper, first, we intend to determine the relationship between the sign of Δ c 0 β y (c 0 + 1) , for 1 < β < 2 , and Δ y (c 0 + 1) > 0 , in the case we assume that Δ c 0 β y (c 0 + 1) is negative. After that, by considering the set D ℓ + 1 , θ ⊆ D ℓ , θ , which are subsets of (1 , 2) , we will extend our previous result to make the relationship between the sign of Δ c 0 β y (z) and Δ y (z) > 0 (the monotonicity of y), where Δ c 0 β y (z) will be assumed to be negative for each z ∈ N c 0 T : = { c 0 , c 0 + 1 , c 0 + 2 , ⋯ , T } and some T ∈ N c 0 : = { c 0 , c 0 + 1 , c 0 + 2 , ⋯ } . The last part of this work is devoted to see the possibility of information reduction regarding the monotonicity of y despite the non-positivity of Δ c 0 β y (z) by means of numerical simulation. [ABSTRACT FROM AUTHOR]

Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately evident that the method is fast and memory-efficient. Moreover, the method's design is such that good convergence properties may be expected. In this paper, we commence a systematic investigation of these convergence properties. [ABSTRACT FROM AUTHOR]

The main metabolism of yeasts produces bioethanol. Bioethanol, which is produced from biomass and bioenergy crops, has been promoted as one of the most viable alternatives to fossil fuels. The following reaction represents all of the knowledge we have regarding intracellular reactions and their regulatory mechanisms: b i o m a s s + s u b s t r a t e s → e t h a n o l + b i o m a s s (m o r e c e l l s). Atangana has suggested new operators based on a combination of fractional and fractal calculus. Fractal-fractional operators (FFOs) have frequently been utilized to investigate the dynamics of a physical problem. In this paper, FFOs are used to investigate a nonlinear mathematical model for ethanol production with three different kernels. Famous fixed point results are employed to show the existence and uniqueness of the solution of the FFO ethanol model under the Mittag–Leffler kernel. The concept of non-linear analysis is utilized to demonstrate the model's Ulam–Hyres stability. The Adams—Bashforth numerical technique, which is based on the Lagrangian interpolation method, is utilized to find the solution of the model under fractal-fractional operators with three different kernels. The numerical results are simulated with MATLAB-17 for several sets of fractional orders and fractal dimensions to show the relationship between components of ethanol production under new operators in various senses. [ABSTRACT FROM AUTHOR]

This research presents a closed-form mathematical framework for assessing the performance of a wireless communication system in the presence of multipath fading channels with an instantaneous signal-to-noise ratio (SNR) subjected to the inverse power Lomax (IPL) distribution. It is demonstrated that depending on the channel parameters, such a model can describe both severe and light fading covering most cases of the well-renowned simplified models (i.e., Rayleigh, Rice, Nakagami-m, Hoyt, α − μ , Lomax, etc.). This study provides the exact results for a basic statistical description of an IPL channel, including the PDF, CDF, MGF, and raw moments. The derived representation was further used to assess the performance of a communication link. For this purpose, the exact expression and their high signal-to-noise ratio (SNR) asymptotics were derived for the amount of fading (AoF), outage probability (OP), average bit error rate (ABER), and ergodic capacity (EC). The closed-form and numerical hyper-Rayleigh analysis of the IPL channel is performed, identifying the boundaries of weak, strong, and full hyper-Rayleigh regimes (HRRs). An in-depth analysis of the system performance was carried out for all possible fading channel parameters' values. The practical applicability of the channel model was supported by comparing it with real-world experimental results. The derived expressions were tested against a numerical analysis and statistical simulation and demonstrated a high correspondence. [ABSTRACT FROM AUTHOR]

In the current study, we compute some upper bounds for the remainder term of Boole's quadrature rule involving convex mappings. First, we build a new identity for first-order differentiable mapping, an auxiliary result to establish our required estimates. We provide several upper bounds by utilizing the identity, convexity property, and bounded property of mappings and some well-known inequalities. Moreover, based on our primary findings, we deliver applications to the means, quadrature rule, special mappings, and non-linear analysis by developing a novel iterative scheme with cubic order of convergence. To the best of our knowledge, the current study is the first attempt to derive upper bounds for Boole's scheme involving convex mappings. [ABSTRACT FROM AUTHOR]

This study introduces a novel approach to enhance variable selection in Data Envelopment Analysis (DEA), especially in stochastic environments where efficiency estimation is inherently complex. To address these challenges, we propose a game cross-DEA model to refine efficiency estimation. Additionally, we integrate the Akaike Information Criterion (AIC) with the Optimal Computing Budget Allocation (OCBA) technique, creating a hybrid method named OCBA–AIC. This innovative method efficiently allocates computational resources for stochastic variable selection. Our numerical analysis indicates that OCBA–AIC surpasses existing methods, achieving a lower AIC value. We also present two real-world case studies that demonstrate the effectiveness of our approach in ranking suppliers and tourism companies under uncertainty by selecting the most suitable partners. This research enriches the understanding of efficiency measurement in DEA and makes a substantial contribution to the field of performance management and decision-making in stochastic contexts. [ABSTRACT FROM AUTHOR]

In interval data envelopment analysis (DEA), the production possibility set is variable, which causes traditional resource allocation optimization methods to yield results with limited reachability. This study aims to improve existing resource allocation optimization models so that they can produce meaningful results when handling interval data. Addressing this topic can enhance the applicability of existing models and improve decision-making accuracy. We grouped decision-making units (DMUs) based on heterogeneity to form production possibility sets. We then considered the characteristics of the worst and best production possibility sets in the interval DEA to establish multiple benchmark fronts. A staged optimization procedure is proposed; the procedure provides a continuous optimization solution, offering a basis for decision-makers to formulate strategies. To illustrate this, we provide a numerical example analysis and a case study on forest carbon sequestration. Finally, by applying our method to China's forest carbon sink data, we show that it better meets the practical needs in China. The practical implication of this procedure is that it provides a basis for decision makers to formulate strategies based on interval data. The theoretical implication is that it extends the application of DEA models to interval data. [ABSTRACT FROM AUTHOR]

In this work, we examine the thermo-magnetic characteristics and energy spectra of a system exposed to both magnetic and Aharonov–Bohm (AB) fields with the existence of an interaction potential that is pseudo-harmonic. Explicit calculations of the eigen-solutions are performed with the expanded Nikiforov–Uvarov formalism. The confluent Heun function is used to represent the equivalent wave functions. If the AB and magnetic fields are gone, quasi-degeneracy in the system's energy levels is shown by a numerical analysis of the energy spectrum. Additionally, we provided a visual representation of how the AB and magnetic fields affected the system's thermo-magnetic characteristics. Our results show a strong dependence of thermo-magnetic properties on temperature, screening parameters, external magnetic fields, and AB fields. [ABSTRACT FROM AUTHOR]

Gravity and flexibility will cause fluctuations of the rotation angle in the servo system for flexible manipulators. The fluctuation will seriously affect the motion accuracy of end-effectors. Therefore, this paper adopts a control method combining the RBF (Radial Basis Function) neural network and pole placement strategy to suppress the rotation angle fluctuations. The RBF neural network is used to identify uncertain items caused by the manipulator's flexibility and the time-varying characteristics of dynamic parameters. Besides, the pole placement strategy is used to optimize the PD (Proportional Differential) controller's parameters to improve the response speed and stability. Firstly, a dynamic model of flexible manipulators considering gravity is established based on the assumed mode method and Lagrange's principle. Then, the system's control characteristics are analyzed, and the pole placement strategy optimizes the parameters of the PD controllers. Next, the control method based on the RBF neural network is proposed, and the Lyapunov stability theory demonstrates stability. Finally, numerical analysis and control experiments prove the effectiveness of the control method proposed in this paper. The means and standard deviations of rotation angle error are reduced by the control method. The results show that the control method can effectively reduce the rotation angle error and improve motion accuracy. [ABSTRACT FROM AUTHOR]